PDE Seminar

TITLE: Optimal Control and Analysis of a Coupled ODE/PDE Immuno-epidemiological Model

ABSTRACT: Optimal control can be used to design intervention strategies for the management of infectious diseases, and has been applied in immunological and epidemiologi-cal models separately. We formulate an immuno-epidemiological model of coupled within-host model of ODEs and between-host model of ODE and PDE. Existence and uniqueness of solution to the between-host model is established, and explicit expressions for the basic reproduction numbers of the within-host and between-host models are derived. Stability of disease-free and endemic equilibria of the between-host model is investigated. An optimal control problem with drug treatment control on the within-host system is formulated and analyzed. Numerical simulations based on the forward-backward sweep method are obtained.